It depends on the ROM. If it's written to be installed with TWRP, you have to st least boot TWRP. If your phone has an unlockable bootloader, you can use fastboot to boot the TWRP img file. The problem is that installing TWRP requires unlocking the bootloader which wipes the phone, so doing a backup that way is a bit impossible. So back everything up using TB, then - if the ROM has to be installed with TWRP, unlock the bootloader, boot the img file, which will leave you running TWRP, install the ROM, clear the system cache unless a dirty flash is recommended, then wen you restart, you'll be in the new ROM with no TWRP. (Or boot to TWRP, then use TWRP to install the TWRP zip file, if you want TWRP permanently installed.)
If the ROM doesn't require TWRP to install it (some can be installed from the "install from zip" from recovery), you don't need TWRP at all, as log as you back up with TB.
But back up with something. Almost all ROMs install as clean ROMs - your data is effectively wiped.